| These diagrams can be used to prove the Pythagorean theorem, which states that if a right triangle has sides of length A and B, and a hypotenuse of length C, then A2 + B2 = C2. Figure 1 and Figure 2 each have four right triangles with sides of length A and B, and a hypotenuse of length C. Since the Figure 1 and Figure 2 both have the same area, removing the four triangles from Figure 1 leaves a region that must have the same area as the region that is left when the four triangles are removed from Figure 2. The area of the region left in Figure 1 is A2 + B2, and the area of the region left in Figure 2 is C2. Thus A2 + B2 = C2, proving the Pythagorean Theorem. |
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